Here is the full list of all 18 Brave Soldier - there are Invasion of Cyborgs achievements.
Explode 10 Explosive Barrels!
Finish the first level!
Kill 5 enemies!
Kill 50 enemies!
Finish 5 levels!
Defeat the Cyborg Golem!
Finish 15 levels!
Defeat the Cyborg Yeti!
Finish 25 levels!
Defeat the Cyborg Skull!
Hold tight to the rope!
Destroy a missile!
Get in the water!
Destroy everything with the special laser!
Die 10 times!
Explode an explosive mine!
Explode an explosive block!
After saving the world, go back to your home!